### Contents

**Banach Algebras, Algebras of Holomorphic Functions, An Introduction.** An Excurs on Banach Algebras. The Algebra of Holomorphic Functions. **General Theory of Fréchet Algebras.** Theory of Fréchet Algebras, Basic Results. General Theory of Uniform Fréchet Algebras. Finitely Generated Fréchet Algebras. Applications of the Projective Limit Representation. A Fréchet Algebra whose Spectrum is not a K-Space. Semisimple Fréchet Algebras. Shilov Boundary and Peak Points for Fréchet Algebras. Michael's Problem. **Analytic Structure in Spectra.** Stein Algebras. Characterizing Some Particular Stein Algebras. Liouville Algebras. Maximum Modulus Principle. Maximum Modulus Algebras and Analytic Structure. Higher Shilov Boundaries. Local Analytic Structure in the Spectrum of a Uniform Fréchet Algebra. Reflexive Uniform Fréchet Algebras. Uniform Fréchet Schwartz Algebras. Appendices: Subharmonic Functions, Poisson Integral. Functional Analysis. References. Index.